Airy Functions And Applications To Physics 2nd Edition
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Airy Functions and Applications to Physics
Author: Olivier Vallée
language: en
Publisher: World Scientific Publishing Company
Release Date: 2004-09-13
The use of special functions, and in particular Airy functions, is rather common in physics. The reason may be found in the need, and even in the necessity, to express a physical phenomenon in terms of an effective and comprehensive analytical form for the whole scientific community. However, for the past twenty years, many physical problems have been resolved by computers. This trend is now becoming the norm as the importance of computers continues to grow. As a last resort, the special functions employed in physics will have to be calculated numerically, even if the analytic formulation of physics is of primary importance. Airy functions have periodically been the subject of many review articles, but no noteworthy compilation on this subject has been published since the 1950s. In this work, we provide an exhaustive compilation of the current knowledge on the analytical properties of Airy functions, developing with care the calculus implying the Airy functions. The book is divided into 2 parts: the first is devoted to the mathematical properties of Airy functions, whilst the second presents some applications of Airy functions to various fields of physics. The examples provided succinctly illustrate the use of Airy functions in classical and quantum physics. Contents:A Historical Introduction: Sir George Biddell AiryDefinitions and PropertiesPrimitives and Integrals of Airy FunctionsTransformations of Airy FunctionsThe Uniform ApproximationGeneralisation of Airy FunctionsApplications to Classical PhysicsApplications to Quantum Physics Readership: Physicists or chemical physicists who use closed and analytical formulae in their field, graduate students in physics and chemical physics.
Airy Functions and Applications to Physics (2nd Edition)
"Addressed mainly to physicist and chemical physicist, this textbook is the result of a broad compilation of current knowledge on analytical properties of Airy functions. In particular, the calculus implying the Airy functions is developed with care. In the latter chapters, examples are given to succinctly illustrate the use of Airy functions in classical and quantum physics. The physicist, for instance in fluid mechanics, can find what he is looking for, in the references for works of molecular physics or in physics of surfaces, and vice versa."--Publisher's website
Basics Of Statistical Physics (Third Edition)
Author: Harald J W Muller-kirsten
language: en
Publisher: World Scientific
Release Date: 2022-03-16
Statistics links microscopic and macroscopic phenomena, and requires for this reason a large number of microscopic elements like atoms. The results are values of maximum probability or of averaging. This introduction to statistical physics concentrates on the basic principles and attempts to explain these in simple terms, supplemented by numerous examples. These basic principles include the difference between classical and quantum statistics, a priori probabilities as related to degeneracies, the vital aspect of indistinguishability as compared with distinguishability in classical physics, the differences between conserved and non-conserved elements, the different ways of counting arrangements in the three statistics (Maxwell-Boltzmann, Fermi-Dirac, Bose-Einstein), the difference between maximization of the number of arrangements of elements, and averaging in the Darwin-Fowler method. Significant applications to solids, radiation and electrons in metals are treated in separate chapters, as well as Bose-Einstein condensation. In this latest edition, apart from a general revision, the topic of thermal radiation has been expanded with a new section on black bodies and an additional chapter on black holes. Other additions are more examples with applications of statistical mechanics in solid state physics and superconductivity. Throughout the presentation, the introduction carries almost all details for calculations.